Sound Propagation in Semimetals under Strong Magnetic Field

Abstract

The electron (hole)-phonon coupling and the dispersion relation of sound wave in semimetals under strong magnetic field are discussed. The discussion is based on an appropriate model from which the direct influence of conduction carriers on the sound propagation and on the carrier-phonon coupling can be separately taken out. Renormalization procedure through the polarization effects by the Coulomb interaction is carried out in the random phase approximation, which is shown to be applicable to the conduction carriers in bismuth. An anomalous behavior in phonon frequency takes place in a different form from the one in a previous work by Blank and Kaner. This anomaly in the quantum limit is explicitly calculated, taking the spin splitting into account. It is seen that depending on the relative magnitude of the effective spin mass to the orbital mass, the anomalous behavior may occur in longer region or in the shorter one of phonon wave-length.